The gain of an idealized Yagi array

Abstract

An expression is derived for the power gain over a doublet of an end-fire array having an infinite number of infinitely closely spaced elements, the currents in successive elements being constant in amplitude but progressively and uniformly retarded in phase, thereby forming a “current sheet” of variable phase in the direction at right angles to the current flow.The power gain is obtained from the integration over an infinite sphere of the Poynting vector resulting from a current of unit amplitude flowing in each element of the array, which gives the total power radiated and comparing this power with the power which must be fed to a doublet to produce the same field strength at the same distance along the axis of the array.Curves are plotted showing the variation of gain with overall length of the array for a number of values of phase velocity. From the envelope of these curves, the maximum gain for a given length of array and the corresponding value of phase velocity are derived.